Question

In: Operations Management

J.C.​ Howard's medical testing company in Kansas wishes to assign a set of jobs to a...

J.C.​ Howard's medical testing company in Kansas wishes to assign a set of jobs to a set of machines. The following table provides the production data of each machine when performing the specific​ job:

                                                            Machine

Job

A

B

C

D

1

9

10

7

6

2

11

5

9

6

3

9

11

5

12

4

12

8

13

9

​a) The optimal assignment of jobs to machine that will maximize total production​ is:

MACHINE A          =   JOB 1, 2, 3, 4 ?

MACHINE B         =    JOB 1, 2, 3, 4 ?

MACHINE C          =   JOB 1, 2, 3, 4 ?

MACHINE D          =   JOB 1, 2, 3, 4 ?

​b) The total production of the assignment​ = __ units ​(enter your response as a whole​ number).

                         

Solutions

Expert Solution

Ans:

a. Machine A = Job 2

Machine B = Job 1

Machine C = Job 4

Machine D = Job 3

b. The total production of the assignment = 46 units

Explanation:

This problem can be solved using linear programming.

Decision Variables:

Pij be number of job i done by machine j.

Job A B C D
1 P11 P12 P13 P14
2 P21 P22 P23 P24
3 P31 P32 P33 P34
4 P41 P42 P43 P44
Job A B C D
1 9 10 7 6
2 11 5 9 6
3 9 11 5 12
4 12 8 13 9

Objective Function: Maximize the production

Zmax = 9P11+10P12+7P13+6P14+11P21+5P22+9P23+6P24+9P31+11P32+5P33+12P34+12P41+8P42+13P43+9P44

Subject to constraints:

The constraint is at max 1 job is assigned to one machine and vice versa.

9P11+10P12+7P13+6P14 <= 1

11P21+5P22+9P23+6P24 <= 1

9P31+11P32+5P33+12P34 <= 1

12P41+8P42+13P43+9P44 <= 1

9P11+11P21+9P31+12P41 <= 1

10P12+5P22+11P32+8P42 <=1

7P13+9P23+5P33+13P43 <=1

6P14+6P24+12P34+9P44 <=1

Pij >= 0

Solving in solver:

Solver Parameters:

Solution:

Formulae:

keosha answered 1 month ago
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